Taxas Relacionadas, Derivadas como Transformações Lineares e Aplicações

Abstract

This work presents the derivatives of functions of several variables and highlights their appli- cations. Its main objective is to present two applications, namely, related rates and function

approximations, and seeking to determine a generalization of the derivation for more general

functions. For this, the fundamental concepts of differential calculus are presented and vari- ous types of problems related to related rates are exposed, as well as a notion of derivation of

functions of several variables, which here are linear transformations and, extends, in a certain

sense, the notion of derivative for functions of one variable. The methodology used in this mo- nograph is exploratory, bibliographical, and the approach is qualitative. The results allowed us

to create an appendix containing a diagram that shows a general algorithm for solving problems involving related rates, since most cases follow the same resolution process, which makes the development of an “algorithm” possible. As a result, this research shows that derivatives make it possible to find good approximations of the image of a function around a point.